Integration schemes for von-mises plasticity models based on exponential maps: Numerical investigations and theoretical considerations

International Journal for Numerical Methods in Engineering

Volumn 64, Issue 9, 2005, Pages 1133-1165

  Artioli, E ^a   Auricchio, F ^b,c   Beirao da Veiga L ^d  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF PAVIA   (Italy)

^c CNR   (Italy)

^d UNIVERSITY OF MILAN   (Italy)

Author keywords

Exact integration; Exponential integration algorithm; Integration factor; Plasticity; Return map

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; HARDENING; INTEGRATION; KINEMATICS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NUMERICAL ANALYSIS; NUMERICAL METHODS; STRAIN MEASUREMENT; STRESSES;

EXPONENTIAL INTEGRATION ALGORITHM; EXPONENTIAL MAP; INTEGRATION FACTOR; ISOTROPIC HARDENING; RETURN MAP; VON-MISES PLASTICITY;

ELASTOPLASTICITY;

MATHEMATICAL MODELING; PLASTICITY;

EID: 27644578705     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1342     Document Type: Article

References (20)

1. Hong-Ki Hong, Chien-Shan Liu. Internal symmetry in bilinear elastoplasticity. International Journal of Non-Linear Mechanics 1999; 34:279-288.
2. Auricchio F, Beirão da Veiga L. On a new integration scheme for von-mises plasticity with linear hardening. International Journal for Numerical Methods in Engineering 2003; 56:1375-1396.
3. Chaboche JL. Constitutive equations for cyclic plasticity and cyclic visco-plasticity. International Journal of Plasticity 1989; 5:247-302.
4. Lubliner J. Plasticity Theory. Macmillan: New York, 1990.
5. Simo JC, Hughes TJR. Computational Inelasticity. Springer: Berlin, 1998.
6. Simo JC. Topics on the numerical analysis and simulation of plasticity. In Handbook of Numerical Analysis, Ciarlet PG, Lions JL (eds), vol. III. Elsevier: Amsterdam, 1999.
7. Auricchio F, Taylor RL. Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity. International Journal of Plasticity 1995; 11:65-98.
8. Zienkiewicz OC, Taylor RL. The Finite Element Method (5th edn), vol. II. McGraw-Hill: New York, 2002.
9. Hong-Ki Hong, Chien-Shan Liu. Internal symmetry in the constitutive model of perfect elastoplasticity. International Journal of Non-Linear Mechanics 2000; 35:447-466.
10. Chien-Shan Liu. Cone of non-linear dynamical system and group preserving schemes. International Journal of Non-Linear Mechanics 2001; 36:1047-1068.
11. Auricchio F. Ce-driver. Technical Report, Dipartimento di Meccanica Strutturale - University of Pavia, 2001. Manual prepared for the European school of advanced studies of seismic risk reduction.
12. Taylor RL. A finite-element analysis program. Technical Report, University of California at Berkeley, 2000. http://www.ce.berkeley.edu/ r1t
13. Krieg RD, Krieg DB. Accuracies of numerical solution methods for the elastic-perfectly plastic model. Journal of Pressure Vessel Technology (ASME) 1977; 99:510-515.
14. Yoder PJ, Whirley RG. On the numerical implementation of elastoplastic models. Journal of Applied Mechanics 1984; 51:283-288.
15. Montmitonnet P, Gratacos P, Chenot JL. An integration scheme for Prandtl-Reuss elastoplasic constitutive equations. International Journal for Numerical Methods in Engineering 1992; 33:943-961.
16. Ristinmaa M, Tryding J. Exact integration of constitutive equations in elasto-plasticity. International Journal for Numerical Methods in Engineering 1993; 36:2525-2544.
17. Wei Z, Peric D, Owen DRJ. Consistent linearization for the exact stress update of Prandtl-Reuss non-hardening elastoplastic models. International Journal for Numerical Methods in Engineering 1996; 39: 1219-1235.
18. Diele F, Lopez L, Peluso R. The Cayley transform in the numerical solution of unitary differential systems. Advances in Computational Mathematics 1998; 8:317-334.
19. Artioli E, Auricchio F, Beirão da Veiga. L. Exponential-based integration algorithms for von-Mises plasticity with linear hardening. Part I: numerical tests on a novel 'optimal' scheme, submitted.
20. Artioli E, Auricchio F, Beirão da Veiga L. Exponential-based integration algorithms for von-Mises plasticity with linear hardening. Part II: consistency, accuracy and stability analysis, submitted.